The Standard & Poor's 500 index also was weighed down by energy shares, while investors took a positive view of the financial sector, sending bank stocks higher.
Shares of oilfield services company Schlumberger Ltd fell after it agreed to buy Smith International Inc for $11.34 billion in stock, which some analysts said was too high.
Schlumberger shares tumbled 5.7 percent to $60.23 and led declines on the S&P energy index <.GSPE>, which fell 1.4 percent. Smith International rose 6.6 percent to $40.20.
Fed Chairman Ben Bernanke is scheduled to testify on the Fed's rate hike and monetary policy in general before House and Senate committees on Wednesday and Thursday.
The market is still processing a lot of the news on the rate increase. It does seems like there's a little concern, said Dennis Cajigas, senior market strategist at Lind-Waldock, a retail brokerage firm in Chicago.
People are still trying to figure out what the intentions of Bernanke are moving forward, Cajigas said.
The Dow Jones industrial average <.DJI> dropped 14.21 points, or 0.14 percent, to 10,388.14. The Standard & Poor's 500 Index <.SPX> dropped 2.09 points, or 0.19 percent, to 1,107.08. The Nasdaq Composite Index <.IXIC> fell 3.90 points, or 0.17 percent, to 2,239.97.
Banks shares continued to rise as the Fed's move was seen as a vote of confidence in the financial system. But overall, investors worried that the rate increase was the first move to withdraw an easy money policy that has helped boost Wall Street, keeping the market's gains in check.
Wells Fargo & Co rose 1.6 percent to $27.81 and the KBW bank index <.BKX> added 1.2 percent.
An index of health insurance stocks <.HMO> rose 1.4 percent after President Barack Obama proposed a revised overhaul of U.S. healthcare.
The lack of a public plan in the president's proposal was a relief for (healthcare) investors, said John Sullivan, healthcare investment strategist at Leerink Swann in Boston.
(Additional reporting by Ellis Mnyandu; Editing by Kenneth Barry)